Question: Given $ m \angle QPR = 2x + 122$, and $ m \angle RPS = 2x + 22$, find $m\angle RPS$. $P$ $Q$ $S$ $R$
Explanation: From the diagram, we see that together ${\angle QPR}$ and ${\angle RPS}$ form ${\angle QPS}$ , so $ {m\angle QPR} + {m\angle RPS} = {m\angle QPS}$ Since $\angle QPS$ is a straight angle, we know ${m\angle QPS = 180}$ Substitute in the expressions that were given for each measure: $ {2x + 122} + {2x + 22} = {180}$ Combine like terms: $ 4x + 144 = 180$ Subtract $144$ from both sides: $ 4x = 36$ Divide both sides by $4$ to find $x$ $ x = 9$ Substitute $9$ for $x$ in the expression that was given for $m\angle RPS$ $ m\angle RPS = 2({9}) + 22$ Simplify: $ {m\angle RPS = 18 + 22}$ So ${m\angle RPS = 40}$.